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Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows
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作者 Luciano K.Araki Rafael B.de R.Borges +1 位作者 Nicholas Dicati P.da Silva Chi-Wang Shu 《Communications on Applied Mathematics and Computation》 EI 2024年第1期533-549,共17页
Capturing elaborated flow structures and phenomena is required for well-solved numerical flows.The finite difference methods allow simple discretization of mesh and model equations.However,they need simpler meshes,e.g... Capturing elaborated flow structures and phenomena is required for well-solved numerical flows.The finite difference methods allow simple discretization of mesh and model equations.However,they need simpler meshes,e.g.,rectangular.The inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular meshes.High-resolution and high-order methods can capture elaborated flow structures and phenomena.They also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation concepts.We perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)schemes.Thus,we propose to solve a challenging engineering application without turbulence models.We aim to verify and validate recent high-resolution and high-order methods.To check the solver accuracy,we solved vortex and Couette flows.Then,we solved inviscid and viscous nozzle flows for a conical profile.We employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving Runge-Kutta.We showed the solver is high-order and captured elaborated flow structures and phenomena.One can see oblique shocks in both nozzle flows.In the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows. 展开更多
关键词 HIGH-RESOLUTION COMPRESSIBLE NAVIER-STOKES Free-shock separation Nozzle flow
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A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES 被引量:2
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作者 Duong Viet THONG Vu Tien DUNG 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期184-204,共21页
In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient ext... In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis. 展开更多
关键词 subgradient extragradient method inertial method variational inequality problem pseudomonotone mapping strong convergence convergence rate
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Analysis and Numerical Computations of the Multi-Dimensional,Time-Fractional Model of Navier-Stokes Equation with a New Integral Transformation
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作者 Yuming Chu Saima Rashid +3 位作者 Khadija Tul Kubra Mustafa Inc Zakia Hammouch M.S.Osman 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第9期3025-3060,共36页
The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is an... The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is analyzed by employing Caputo fractional derivative.We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods,respectively.The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems.The exact and estimated solutions are delineated via numerical simulation.The proposed analysis indicates that the projected configuration is extremely meticulous,highly efficient,and precise in understanding the behavior of complex evolutionary problems of both fractional and integer order that classify affiliated scientific fields and technology. 展开更多
关键词 Caputo derivative Elzaki transform time-fractional Navier-Stokes equation decomposition method
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A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws
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作者 Liang Li Jun Zhu +1 位作者 Chi-Wang Shu Yong-Tao Zhang 《Communications on Applied Mathematics and Computation》 2023年第1期403-427,共25页
Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternati... Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions. 展开更多
关键词 Fixed-point fast sweeping methods Multi-resolution WENO schemes Steady state ILW procedure Convergence
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Preface to the Focused Issue in Honor of Professor Tong Zhang on the Occasion of His 90th Birthday
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作者 Jiequan Li Wancheng Sheng +2 位作者 Chi-Wang Shu Ping Zhang Yuxi Zheng 《Communications on Applied Mathematics and Computation》 2023年第3期965-966,共2页
December 9,2022 is the 90th birthday of Tong Zhang,a mathematician in Institute of Mathematics,Chinese Academy of Sciences where he was always working on the Riemann problem for gas dynamics in his mathematical life.T... December 9,2022 is the 90th birthday of Tong Zhang,a mathematician in Institute of Mathematics,Chinese Academy of Sciences where he was always working on the Riemann problem for gas dynamics in his mathematical life.To celebrate his 90th birthday and great contributions to this specifc feld,we organize this focused issue in the journal Communications on Applied Mathematics and Computation,since the Riemann problem has been proven to be a building block in all felds of theory,numerics and applications of hyperbolic conservation laws. 展开更多
关键词 RIEMANN HYPERBOLIC Focus
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Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems
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作者 Paula Chen Jerome Darbon Tingwei Meng 《Communications on Applied Mathematics and Computation》 EI 2024年第2期1428-1471,共44页
Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we p... Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control.We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians.Additionally,we present an efficient,grid-free numerical solver based on our representation formulas,which is shown to scale linearly with the state dimension,and thus,to overcome the curse of dimensionality.Using existing optimization methods and the min-plus technique,we extend our numerical solvers to address more general classes of convex and nonconvex initial costs.We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit(CPU)and a field-programmable gate array(FPGA).In several cases,our FPGA implementation obtains over a 10 times speedup compared to the CPU,which demonstrates the promising performance boosts FPGAs can achieve.Our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time. 展开更多
关键词 Optimal control Hamilton-Jacobi partial differential equations Grid-free numerical methods High dimensions Field-programmable gate arrays(FPGAs)
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Efficient Finite Difference WENO Scheme for Hyperbolic Systems withNon-conservativeProducts
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作者 Dinshaw S.Balsara Deepak Bhoriya +1 位作者 Chi-Wang Shu Harish Kumar 《Communications on Applied Mathematics and Computation》 EI 2024年第2期907-962,共56页
Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of ... Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages. 展开更多
关键词 Hyperbolic PDEs Numerical schemes Non-conservative products Stiff source terms Finite difference WENO
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RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes
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作者 Jun Zhu Chi-Wang Shu Jianxian Qiu 《Communications on Applied Mathematics and Computation》 EI 2024年第3期1575-1599,共25页
In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state pr... In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems. 展开更多
关键词 RKDG method Steady-state problem Multi-resolution WENO limiter Triangular mesh Machine zero
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THEORY OF WATER WAVES IN AN ELASTIC VESSEL 被引量:4
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作者 D. Y. Hsieh 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2000年第2期97-112,共16页
Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Base... Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the on- set of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and nu- merical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by tile high-frequency external excitation. 展开更多
关键词 water waves elastic vessel Dragon Wash
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Numerical simulations of compressible mixing layers with a discontinuous Galerkin method 被引量:6
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作者 Xiao-Tian Shi Jun Chen +2 位作者 Wei-Tao Bi Chi-Wang Shu Zhen-Su She 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第3期318-329,共12页
Discontinuous Galerkin(DG) method is known to have several advantages for flow simulations,in particular,in fiexible accuracy management and adaptability to mesh refinement. In the present work,the DG method is deve... Discontinuous Galerkin(DG) method is known to have several advantages for flow simulations,in particular,in fiexible accuracy management and adaptability to mesh refinement. In the present work,the DG method is developed for numerical simulations of both temporally and spatially developing mixing layers. For the temporally developing mixing layer,both the instantaneous fiow field and time evolution of momentum thickness agree very well with the previous results. Shocklets are observed at higher convective Mach numbers and the vortex paring manner is changed for high compressibility. For the spatially developing mixing layer,large-scale coherent structures and self-similar behavior for mean profiles are investigated. The instantaneous fiow field for a three-dimensional compressible mixing layer is also reported,which shows the development of largescale coherent structures in the streamwise direction. All numerical results suggest that the DG method is effective in performing accurate numerical simulations for compressible shear fiows. 展开更多
关键词 Compressible mixing layer - Discontinuous Galerkin method . Self-similarity . Coherent structure
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LESSER KNOWN MIRACLES OF BURGERS EQUATION 被引量:1
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作者 Govind Menon 《Acta Mathematica Scientia》 SCIE CSCD 2012年第1期281-294,共14页
This article is a short introduction to the surprising appearance of Burgers equation in some basic probabilistic models.
关键词 Burgers equation random matrix theory kinetic theory Dyson's Brownianmotion Kerov's kinetic equation shock clustering integrable systems
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Dynamic Response of Floating Body Subjected to Underwater Explosion Bubble and Generated Waves with 2D Numerical Model 被引量:1
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作者 Zhaoli Tian Yunlong Liu +2 位作者 Shiping Wang A Man Zhang Youwei Kang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2019年第2期397-423,共27页
The low frequency load of an underwater explosion bubble and the generated waves can cause significant rigid motion of a ship that threaten its stability.In order to study the fluid-structure interaction qualitatively... The low frequency load of an underwater explosion bubble and the generated waves can cause significant rigid motion of a ship that threaten its stability.In order to study the fluid-structure interaction qualitatively,a two-dimensional underwater explosion bubble dynamics model,based on the potential flow theory,is established with a double-vortex model for the doubly connected bubble dynamics simulation,and the bubble shows similar dynamics to that in 3-dimensional domain.A fully nonlinear fluid-structure interaction model is established considering the rigid motion of the floating body using the mode-decomposition method.Convergence test of the model is implemented by simulating the free rolling motion of a floating body in still water.Through the simulation of the interaction of the underwater explosion bubble,the generated waves and the floating body based on the presented model,the influences of the buoyancy parameter and the distance parameter are discussed.It is found that the impact loads on floating body caused by underwater explosion bubble near the free surface can be divided into 3 components:bubble pulsation,jet impact,and slamming load of the generated waves,and the intensity of each component changes nonlinearly with the buoyance parameter.The bubble pulsation load decays with the increase in the horizontal distance.However,the impact load from the generated waves is not monotonous to distance.It increases with the distance within a particular distance threshold,but decays thereafter. 展开更多
关键词 UNDERWATER explosion BUBBLE DYNAMICS fluid-structure INTERACTION double-vortex model WAVES GENERATED by UNDERWATER explosion.
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STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES 被引量:1
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作者 Nguyen Xuan LINH Duong Viet THONG +2 位作者 Prasit CHOLAMJIAK Pham Anh TUAN Luong Van LONG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第2期795-812,共18页
In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our me... In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems. 展开更多
关键词 Inertial method Tseng’s extragradient viscosity method variational inequality problem pseudomonotone mapping strong convergence
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Convergence to Steady-State Solutions of the New Type of High-Order Multi-resolution WENO Schemes: a Numerical Study 被引量:2
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作者 Jun Zhu Chi-Wang Shu 《Communications on Applied Mathematics and Computation》 2020年第3期429-460,共32页
A new type of high-order multi-resolution weighted essentially non-oscillatory(WENO)schemes(Zhu and Shu in J Comput Phys,375:659-683,2018)is applied to solve for steady-state problems on structured meshes.Since the cl... A new type of high-order multi-resolution weighted essentially non-oscillatory(WENO)schemes(Zhu and Shu in J Comput Phys,375:659-683,2018)is applied to solve for steady-state problems on structured meshes.Since the classical WENO schemes(Jiang and Shu in J Comput Phys,126:202-228,1996)might suffer from slight post-shock oscillations(which are responsible for the residue to hang at a truncation error level),this new type of high-order finite-difference and finite-volume multi-resolution WENO schemes is applied to control the slight post-shock oscillations and push the residue to settle down to machine zero in steady-state simulations.This new type of multi-resolution WENO schemes uses the same large stencils as that of the same order classical WENO schemes,could obtain fifth-order,seventh-order,and ninth-order in smooth regions,and could gradually degrade to first-order so as to suppress spurious oscillations near strong discontinuities.The linear weights of such new multi-resolution WENO schemes can be any positive numbers on the condition that their sum is one.This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finitedifference and finite-volume WENO schemes for solving steady-state problems.In comparison with the classical fifth-order finite-difference and finite-volume WENO schemes,the residue of these new high-order multi-resolution WENO schemes can converge to a tiny number close to machine zero for some benchmark steady-state problems. 展开更多
关键词 High-order multi-resolution WENO scheme Unequal-sized hierarchical stencil Central spatial stencil Steady-state problem
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Superconvergence of Energy-Conserving Discontinuous Galerkin Methods for Linear Hyperbolic Equations 被引量:1
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作者 Yong Liu Chi-Wang Shu Mengping Zhang 《Communications on Applied Mathematics and Computation》 2019年第1期101-116,共16页
In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges t... In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges to a particular projection of the exact solution.The order of this superconvergence is proved to be k+2 when piecewise Pk polynomials with K≥1 are used.The proof is valid for arbitrary non-uniform regular meshes and for piecewise polynomials with arbitrary K≥1.Furthermore,we find that the derivative and function value approxi?mations of the DG solution are superconvergent at a class of special points,with an order of k+1 and R+2,respectively.We also prove,under suitable choice of initial discretization,a(2k+l)-th order superconvergence rate of the DG solution for the numerical fluxes and the cell averages.Numerical experiments are given to demonstrate these theoretical results. 展开更多
关键词 Energy-conserving DISCONTINUOUS GALERKIN methods SUPERCONVERGENCE Linear HYPERBOLIC equations
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Colouring of COVID-19 Affected Region Based on Fuzzy Directed Graphs 被引量:1
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作者 Rupkumar Mahapatra Sovan Samanta +4 位作者 Madhumangal Pal Jeong-Gon Lee Shah Khalid Khan Usman Naseem Robin Singh Bhadoria 《Computers, Materials & Continua》 SCIE EI 2021年第7期1219-1233,共15页
Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-w... Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,etc.Nowadays,social networks are prevalent systems in our life.Here,the users are considered as vertices,and their connections/interactions are taken as edges.Some users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular profiles.That means,along with traditional relationship(information flowing),there is another relation among them.It depends on the domination of the relationship between the nodes.This type of situation can be modelled as a directed fuzzy graph.In the colouring of fuzzy graph theory,edge membership plays a vital role.Edge membership is a representation of flowing information between end nodes of the edge.Apart from the communication relationship,there may be some other factors like domination in relation.This influence of power is captured here.In this article,the colouring of directed fuzzy graphs is defined based on the influence of relationship.Along with this,the chromatic number and strong chromatic number are provided,and related properties are investigated.An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs. 展开更多
关键词 Graph colouring chromatic index directed fuzzy graphs
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New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag-Leffler Function in the Kernel
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作者 Saima Rashid Zakia Hammouch +1 位作者 Rehana Ashraf Yu-Ming Chu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第1期359-378,共20页
In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalga... In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering. 展开更多
关键词 Integral inequality generalized fractional integral with respect to another function increasing and decreasing functions Mittag-Leffler function
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Preface: theory, methods, and applications of mesoscopic modeling
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作者 Z. LI Guohui HU G.E. KARNIADAKIS 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第1期1-2,共2页
With increasing attention to complex fluids and soft matter, we have witnessed a fast- growing research in mesoscopic modeling and simulation in the past decades. The development of mesoscopic methods offers many pote... With increasing attention to complex fluids and soft matter, we have witnessed a fast- growing research in mesoscopic modeling and simulation in the past decades. The development of mesoscopic methods offers many potential opportunities as well as challenges in modeling of complex materials for diverse applications. Despite significant progress in the past decade, mesoscopic methods are still under development. New formulation in the models, novel theo- retical interpretations, and innovative numerical algorithms often appear in literature. These mesoscopic methods have been already applied to a large number of problems, including poly- mer and colloidal suspensions, multiphase fluids, biological materials, and blood rheology. New applications of mesoscopic modeling in different areas are still emerging. 展开更多
关键词 THEORY METHODS mesoscopic modeling
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Analysis and Approximation of Gradient Flows Associated with a Fractional Order Gross-Pitaevskii Free Energy
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作者 Mark Ainsworth Zhiping Mao 《Communications on Applied Mathematics and Computation》 2019年第1期5-19,共15页
We establish the well-posedness of the fractional PDE which arises by considering the gradient flow associated with a fractional Gross-Pitaevskii free energy functional and some basic properties of the solution.The eq... We establish the well-posedness of the fractional PDE which arises by considering the gradient flow associated with a fractional Gross-Pitaevskii free energy functional and some basic properties of the solution.The equation reduces to the Allen-Cahn or Cahn-Hilliard equations in the case where the mass tends to zero and an integer order derivative is used in the energy.We study how the presence of a non-zero mass affects the nature of the solutions compared with the Cahn-Hilliard case.In particular,we show that,analogous to the Cahn-Hilliard case,the solutions consist of regions in which the solution is a piecewise constant(whose value depends on the mass and the fractional order)separated by an interface whose width is independent of the mass and the fractional derivative.However,if the average value of the initial data exceeds some threshold(which we determine explic让ly),then the solution will tend to a single constant steady state. 展开更多
关键词 FRACTIONAL differential equation NON-LOCAL energy WELL-POSEDNESS FOURIER spectral method
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Intergenic subset organization within a set of geographically-defined viral sequences from the 2009 H1N1 influenza A pandemic
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作者 William A. Thompson Joel K. Weltman 《American Journal of Molecular Biology》 2012年第1期32-41,共10页
We report a bioinformatic analysis of the datasets of sequences of all ten genes from the 2009 H1N1 influenza A pandemic in the state of Wisconsin. The gene with the greatest summed information entropy was found to be... We report a bioinformatic analysis of the datasets of sequences of all ten genes from the 2009 H1N1 influenza A pandemic in the state of Wisconsin. The gene with the greatest summed information entropy was found to be the hemagglutinin (HA) gene. Based upon the viral ID identifier of the HA gene sequence, the sequences of all of the genes were sorted into two subsets, depending upon whether the nucleotide occupying the position of maximum entropy, position 658 of the HA sequence, was either A or U. It was found that the information entropy (H) distributions of subsets differed significantly from each other, from H distributions of randomly generated subsets and from the H distributions of the complete datasets of each gene. Mutual information (MI) values facilitated identification of nine nucleotide positions, distributed over seven of the influenza genes, at which the nucleotide subsets were disjoint, or almost disjoint. Nucleotide frequencies at these nine positions were used to compute mutual information values that subsequently served as weighting factors for edges in a graph net-work. Seven of the nucleotide positions in the graph network are sites of synonymous mutations. Three of these sites of synonymous mutation are within a single gene, the M1 gene, which occupied the position of greatest graph centrality. It is proposed that these bioinformatic and network graph results may reflect alterations in M1-mediated viral packaging and exteriorization, known to be susceptible to synonymous mutations. 展开更多
关键词 Influenza A H1N1 Bioinformatics Genes PANDEMIC Epidemic Information Entropy MutualInFormation Graph Network CENTRALITY SUBSETS
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